The Q values of double-electron capture in 124Xe, 130Ba, and 136Ce and double-beta decay of 124Sn and 130Te have been determined with the Penning-trap mass spectrometer SHIPTRAP with a few hundred eV uncertainty. These nuclides are members of three isobaric triplets with common daughter nuclides. The main goal of this work was to investigate the existence of the resonant enhancement of the neutrinoless double-electron-capture rates in 124Xe and 130Ba in order to assess their suitability for the search for neutrinoless double-electron capture. Based on our results, in neither of these cases is the resonance condition fulfilled.